Nikki bought a triangular lot whose sides are 9 meters, 12 meters, and 15 meters long. if it cost her 3500 pesos per square meter, how much did she pay for the lot?

right triangle 3, 4 ,5 each times three

base 4, altitude 3

(1/2)4* 4 = 6 m^2

To find the area of the triangular lot, we can use Heron's formula.

Heron's formula states that the area of a triangle with side lengths a, b, and c is given by the formula:

Area = √(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle, which is calculated by:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 9 meters, 12 meters, and 15 meters.

Calculating the semi-perimeter:
s = (9 + 12 + 15) / 2
s = 36 / 2
s = 18 meters

Calculating the area using Heron's formula:
Area = √(18 * (18 - 9) * (18 - 12) * (18 - 15))
Area = √(18 * 9 * 6 * 3)
Area = √(2916)
Area ≈ 54 meters^2

Now, to find the cost, we multiply the area by the cost per square meter:
Cost = Area * Cost per square meter
Cost = 54 meters^2 * 3500 pesos/meter^2
Cost = 189,000 pesos

Therefore, Nikki paid 189,000 pesos for the lot.

To find out how much Nikki paid for the lot, we need to calculate the area of the triangular lot and then multiply it by the cost per square meter.

1. Calculate the area of the triangle using Heron's formula:
- Let a, b, and c be the lengths of the sides of the triangle.
- The semi-perimeter (s) of the triangle is given by s = (a + b + c) / 2.
- The area (A) of the triangle is given by A = sqrt(s(s-a)(s-b)(s-c)), where sqrt denotes the square root.

Given that the lengths of the sides are 9 meters, 12 meters, and 15 meters, we can calculate the area as follows:

s = (9 + 12 + 15) / 2 = 18

A = sqrt(18(18-9)(18-12)(18-15))
= sqrt(18 * 9 * 6 * 3)
= sqrt(2916)
≈ 54 meters squared

2. Now that we have the area of the triangular lot as 54 square meters, we can calculate the total cost:
- The cost per square meter is given as 3500 pesos.

Total cost = Area of the lot * Cost per square meter
= 54 meters squared * 3500 pesos/meter squared
= 189,000 pesos

Therefore, Nikki paid 189,000 pesos for the lot.